Light propagation through time dependent disordered or random media is generally regarded as a randomisation process of the optical field destroying all the information in the initial beam. However, a coherent beam propagating in a stationary random medium yields a deterministic speckle pattern, whilst maintaining its initial spatial and temporal coherence. Such behaviour is exploited in the design of several novel optical devices, for example to create focal spots using computer generated holograms, to trap micro-particles and coherently address plasmonic nano-structures.
Key to devices based on time dependent disordered or random media is that the information content of the optical field is maintained when transmitted through a random medium. Thus, the stationary wavefront randomisation process can be used to detect the state of the light field before scattering.
The use of wavelength meters is ubiquitous in photonics. Miniaturisation of such devices would be highly advantageous. A multimode fiber may be used to create wavefront randomisation to act as a spectrometer, as described in B. Redding, S. M. Popoff, and H. Cao, Opt. Express 21, 6584 (2013), and B. Redding and H. Cao, Opt. Lett. 37, 3384 (2012). However, to achieve a resolution of 8 pm between two adjacent laser lines would require 20 m of fibre free of perturbations, which would be difficult to realize in practice. It has also separately been recognised that spectral polarimetric measurements may be performed using the transmission matrix of random media, see T. W. Kohlgraf-Owens and A. Dogariu, Opt. Lett. 35, 2236 (2010).
Lab-on-a-chip applications require small integrated wavelength detectors. One way to achieve this is by propagating light through periodic structures, such as a super prism made from specially engineered photonic crystals. The optical dispersion of these crystals can deliver resolution of 0.4 nm at a wavelength of 1.5 μm. However, these devices rely on out-of-plane detection and free space propagation, and so are not fully integrated on-chip devices.